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Single photons in an interferometer:Forbidden outcomes

S. van den Hoven

Published Oct 16, 2023• 0 citations
OpenAlex

Abstract

The well-known Hong-Ou-Mandel (HOM) effect is the first demonstration of perfect destructive interference of quantum amplitudes in a linear optical system with single photon Fock-states at input. A natural question to ask is whether we are able to predict similar behavior for systems of a general size, that is, predicting forbidden transitions for a given input state and a given linear optical system. Previous studies have found that certain symmetries between the input and output configuration in combination with a symmetric interferometer will always result into so called suppressions. But recently, a few examples have been found of suppressions which do not obey the suppression laws constructed in previous studies. In this work, we parametrize a general three-mode interferometer and we use a numerical optimization algorithm in order to find all three-mode interferometers that demonstrate forbidden transitions. These results help us to gain a better understanding of the fundamental reason behind suppressions. In addition, we compare the quality of the different interferometers for applications in quantum tomography.

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The well-known Hong-Ou-Mandel (HOM) effect is the first demonstration of perfect destructive interference of quantum amplitudes in a linear optical system with single photon Fock-states at input. A natural question to ask is whether we are able to predict similar behavior for systems of a general size, that is, predicting forbidden transitions for a given input state and a given linear optical system. Previous studies have found that certain symmetries between the input and output configuration in combination with a symmetric interferometer will always result into so called suppressions. But recently, a few examples have been found of suppressions which do not obey the suppression laws constructed in previous studies. In this work, we parametrize a general three-mode interferometer and we use a numerical optimization algorithm in order to find all three-mode interferometers that demonstrate forbidden transitions. These results help us to gain a better understanding of the fundamental reason behind suppressions. In addition, we compare the quality of the different interferometers for applications in quantum tomography.
Photonic interference is a key quantum resource for optical quantum computation, and in particular for so-called boson sampling devices. In interferometers with certain symmetries, genuine multiphoton quantum interference effectively suppresses certain sets of events, as in the original Hong–Ou–Mandel effect. Recently, it was shown that some classical and semi-classical models could be ruled out by identifying such suppressions in Fourier interferometers. Here we propose a suppression law suitable for random-input experiments in multimode Sylvester interferometers, and verify it experimentally using 4- and 8-mode integrated interferometers. The observed suppression occurs for a much larger fraction of input–output combinations than what is observed in Fourier interferometers of the same size, and could be relevant to certification of boson sampling machines and other experiments relying on bosonic interference, such as quantum simulation and quantum metrology.
The investigation of multi-photon quantum interference in symmetric multi-port splitters has both fundamental and applicative interest. Destructive quantum interference in devices with specific symmetry leads to the suppression of a large number of possible output states, generalizing the Hong-Ou-Mandel effect; simple suppression laws have been developed for interferometers implementing the Fourier or the Hadamard transform over the modes. In fact, these enhanced interference features in the output distribution can be used to assess the indistinguishability of single-photon sources, and symmetric interferometers have been envisaged as benchmark or validation devices for Boson-Sampling machines. In this work we devise an innovative approach to implement symmetric multi-mode interferometers that realize the Fourier and Hadamard transform over the optical modes, exploiting integrated waveguide circuits. Our design is based on the optical implementations of the Fast-Fourier and Fast-Hadamard transform algorithms, and exploits a novel three-dimensional layout which is made possible by the unique capabilities of femtosecond laser waveguide writing. We fabricate devices with m = 4 and m = 8 modes and we let two identical photons evolve in the circuit. By characterizing the coincidence output distribution we are able to observe experimentally the known suppression laws for the output states. In particular, we characterize the robustness of this approach to assess the photons' indistinguishability and to rule out alternative non-quantum states of light. The reported results pave the way to the adoption of symmetric multiport interferometers as pivotal tools in the diagnostics and certification of quantum photonic platforms.
Two-photon interference effects arise because photons are indistinguishable particles. In the wellknown Hong-Ou-Mandel (HOM) effect, the transmission of two photons at a beam splitter interferes destructively with the reflection of both photons, requiring both photons to "bunch up" by leaving the beam splitter on the same side. Here, we show that the interference between locally propagating photons and photons exchanged by a mode swap can be implemented by post-selecting spatially separated photon outputs of a four-path interferometer. Even though the photons detected at spatially separated locations must have travelled along paths that never met up at the same beam splitter, the Hong-Ou-Mandel effect can be observed in correlations between the output ports that originate from the association of detection events with non-local output modes defined by the two single photon inputs. Local phase shifts can be used to map out non-classical correlations between the photons detected at different output locations, clarifying the role of linear optics in generating entanglement between spatially separated photons. Our work thus establishes a fundamental relation between multiphoton interference and entanglement, opening the door to new possibilities in optical quantum technologies.
Quantum interference of correlated particles is a fundamental quantum phenomenon which carries signatures of the statistics properties of the particles, such as bunching or antibunching. In the presence of particular symmetries, interference effects take place with high visibility, one of the simplest cases being the suppression of coincident detection in the Hong-Ou-Mandel effect. Tichy et al., [Phys. Rev. Lett. 104, 220405 (2010)] recently demonstrated a simple sufficient criterion for the suppression of output events in the more general case of Fourier multiport beam splitters. Here we study the case in which 2q{2}^{q}2q particles (either bosonic or fermionic) are injected simultaneously in different ports of a Sylvester interferometer with ${2}^{p}\ensuremath{\ge}{2}^{q}$ modes. In particular, we prove a necessary and sufficient criterion for a significant fraction of output states to be suppressed, for specific input configurations. This may find application in assessing the indistinguishability of multiple single-photon sources and in the validation of boson sampling machines.
In recent works we have explored a multi-photon extension of the celebrated two-photon Hong-Ou-Mandel (HOM) effect in which the quantum amplitudes for a two-photon input to a lossless, balanced 50:50 beamsplitter (BS) undergoes complete destructive interference. In the extended Hong-Ou-Mandel (eHOM) effect the multi-photon scattering of photons from the two input ports to the two output ports of the BS for Fock number basis input states (FS) ∣n,m⟩12|n,m\rangle_{12}∣n,m⟩12​ exhibit complete destructive interference pairwise within the quantum amplitudes containing many scattering components, generalizing the two-photon HOM effect. This has profound implications for arbitrary bipartite photonic input states constructed from such basis states: if the input state to one input port of the BS is of odd parity, i.e. constructed from only of odd numbers of photons, then regardless of the input state to the second 50:50 BS port, there will be a central nodal line (CNL) of zeros in the joint output probability distribution along the main diagonal for coincidence detection. The first goal of this present work is to show diagrammatically how the extended HOM effect can be seen as a succession of multi-photon HOM effects when the latter is viewed as a pairwise cancellation of mirror image scattering amplitudes. The second goal of this work is to explore considerations for the experimental realization of the extended Hong-Ou-Mandel effect. We examine the case of a single photon interfering with a coherent state (an idealized laser) on a balanced 50:50 beamsplitter and consider prospects for experimental detection of the output destructive interference by including additional effects such as imperfect detection efficiency, spatio-temporal mode functions, and time delay between the detected output photons.
The Hong-Ou-Mandel (HOM) interference is one of the most fundamental quantum-mechanical effects that reveal a nonclassical behavior of single photons. Two identical photons that are incident on the input ports of an unbiased beam splitter always exit the beam splitter together from the same output port, an effect referred to as photon bunching. In this Letter, we utilize a single electro-optic phase modulator as a probabilistic frequency beam splitter, which we exploit to observe HOM interference between two photons that are in different spectral modes, yet are identical in other characteristics. Our approach enables linear optical quantum information processing protocols using the frequency degree of freedom in photons such as quantum computing techniques with linear optics.